SUO: Complexity Of Intertranslation
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SUOphists,
This is a comment that has been accumulating in my buffer
for quite some time -- indeed, I have made the occasional
allusion to it from time to time, though often in passing,
and most likely buried in the medium of numerous parallel
and transverse asides, but now I believe that it may just
be time to try and make a special point of focusing on it,
in its own right.
By way of moving as quickly as possible to an extremely concrete example,
the following two formal languages are roughly intertranslatable, if you
will excuse the inexpressiveness of the former in regard to the identity
element of the additive group, but making that observation is hardly the
end of the matter when it comes to evaluating their respective utilities
for any purpose under heaven, that is, outside of inscribing dedications
on the cornerstones of buildings, where the aim is the probably illusory
sense of security that accrues to a pretense of continuity with the past,
or else in the final roll of credits on a cinematic production, when the
end is to prevent the casual or time-limited viewer from knowing exactly
how dated indeed the passing show of the spectacle in question really is.
Enough of my perfunctory talk-show chatter -- time to roll the clip!
Language 0 = { I, II, III, IV, V, VI, VII, VIII, IX, X, ...},
Language 1 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...}.
Now, don't get me wrong -- I have no quarrel with the fact that it is
a perfectly good thing to know, insofar as we may speak theoretically,
that these two languages for talking about, or, at least for denoting,
the non-negative integers or natural numbers N, are almost completely
intertranslatable -- it is just that, insofar as we must occasionally
speak practically, there are so many matters that we must think about
that we will just never get around to thinking about, or else be very
sorely afflicted and even more severely impeded, if we find ourselves
forced to stick, so viscously, within the circus romanum of the first
set of numerals.
That is my basic point -- I will have more to say, another time, about the
computational complexity of the (com)putative intertranslations, and about
the bearing that this may have on our selection among several alternatives.
Until Then,
Jon Awbrey
Incidental Musements:
http://www.suoseura.com/
http://www.suoseura.com/englanniksi.html
http://honeybee.helsinki.fi/mmeko/suo_lehti/suo.htm
http://honeybee.helsinki.fi/mmeko/suo_lehti/cont51.htm
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